Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS
Direct usage of construction plans as input for structural analyses assumes the reference configuration to match the engineering drawings. However, the built construction is typically supposed to match the construction plans after its successful erection. In that state, the structure is usually alre...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2022-01-01
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| Series: | Advances in Civil Engineering |
| Online Access: | http://dx.doi.org/10.1155/2022/3573608 |
| _version_ | 1811177893108121600 |
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| author | Klaus Bernd Sautter Kai-Uwe Bletzinger |
| author_facet | Klaus Bernd Sautter Kai-Uwe Bletzinger |
| author_sort | Klaus Bernd Sautter |
| collection | DOAJ |
| description | Direct usage of construction plans as input for structural analyses assumes the reference configuration to match the engineering drawings. However, the built construction is typically supposed to match the construction plans after its successful erection. In that state, the structure is usually already subjected to self-weight and maybe other loadings. Consequently, an analysis approach is necessary to find the unknown reference configuration for a given, desired deformed structural shape. The standard static problem needs to be reformulated with the reference coordinates being the unknown variables. This work describes the necessary steps for geometrically and materially nonlinear truss elements based on the variation of reference strategy (VaReS) and gives a highly detailed description of all resultant system derivatives. Arbitrary hyperelastic material laws can be applied of which this work introduces the St. Venant-Kirchhoff, the Neo-Hookean, and the Ogden law. Additionally, the self-weight load case is considered, increasing the problem’s nonlinearity. Finally, two- and three-dimensional structural problems are presented to show the solution capabilities, ranging from simple 3-bar systems to larger framework bridges. While all necessary vectors and matrices are discussed and presented in great detail, a publicly available GitHub repository makes the code freely accessible as Python code. |
| first_indexed | 2024-04-11T06:08:58Z |
| format | Article |
| id | doaj.art-b1bfd8263a734dd383e7e4c469f6a656 |
| institution | Directory Open Access Journal |
| issn | 1687-8094 |
| language | English |
| last_indexed | 2024-04-11T06:08:58Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Advances in Civil Engineering |
| spelling | doaj.art-b1bfd8263a734dd383e7e4c469f6a6562022-12-22T04:41:23ZengHindawi LimitedAdvances in Civil Engineering1687-80942022-01-01202210.1155/2022/3573608Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReSKlaus Bernd Sautter0Kai-Uwe Bletzinger1Chair of Structural AnalysisChair of Structural AnalysisDirect usage of construction plans as input for structural analyses assumes the reference configuration to match the engineering drawings. However, the built construction is typically supposed to match the construction plans after its successful erection. In that state, the structure is usually already subjected to self-weight and maybe other loadings. Consequently, an analysis approach is necessary to find the unknown reference configuration for a given, desired deformed structural shape. The standard static problem needs to be reformulated with the reference coordinates being the unknown variables. This work describes the necessary steps for geometrically and materially nonlinear truss elements based on the variation of reference strategy (VaReS) and gives a highly detailed description of all resultant system derivatives. Arbitrary hyperelastic material laws can be applied of which this work introduces the St. Venant-Kirchhoff, the Neo-Hookean, and the Ogden law. Additionally, the self-weight load case is considered, increasing the problem’s nonlinearity. Finally, two- and three-dimensional structural problems are presented to show the solution capabilities, ranging from simple 3-bar systems to larger framework bridges. While all necessary vectors and matrices are discussed and presented in great detail, a publicly available GitHub repository makes the code freely accessible as Python code.http://dx.doi.org/10.1155/2022/3573608 |
| spellingShingle | Klaus Bernd Sautter Kai-Uwe Bletzinger Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS Advances in Civil Engineering |
| title | Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS |
| title_full | Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS |
| title_fullStr | Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS |
| title_full_unstemmed | Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS |
| title_short | Hyperelastic Geometrically Nonlinear Inverse 3D-FEM Truss Analyses Based on VaReS |
| title_sort | hyperelastic geometrically nonlinear inverse 3d fem truss analyses based on vares |
| url | http://dx.doi.org/10.1155/2022/3573608 |
| work_keys_str_mv | AT klausberndsautter hyperelasticgeometricallynonlinearinverse3dfemtrussanalysesbasedonvares AT kaiuwebletzinger hyperelasticgeometricallynonlinearinverse3dfemtrussanalysesbasedonvares |